Collaborative Research: Investigating Productive Use of High-Leverage Student Mathematical Thinking

该项目将考察中学数学教师在整个课堂讨论中如何回应和使用学生的思维。教师面临的一个持续挑战是在整个课堂讨论中最大限度地利用学生新出现的数学想法。教师需要利用学生已经形成的思想，以便为学习重要的数学概念创造机会。这项研究将创建专门为教师创造机会的任务，以建立在学生思维的基础上，然后利用课堂观察和课堂视频分析来开发工具，以支持教师领导全班讨论。探索研究K-12计划(DRK-12)旨在通过研究和开发创新资源、模型和工具(RMT)，显著提高K-12学龄前学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。DRK-12计划的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，这些研究和开发工作为拟议的项目提供了理论和实证证明。该项目侧重于建立在学生思维基础上的教学实践，即教师让学生理解同龄人的数学思想的实践，帮助整个班级在数学理解方面取得进展。本研究探讨了教师如何将这一实践融入中学数学课堂讨论中，方法是设计任务，使教师有机会发展学生的思维，并研究教师如何围绕学生对这些任务的反应来安排整个班级的讨论。该项目让教师和研究人员共同探索建筑实践。教师和研究人员将在自己的课堂上使用项目设计的任务，然后与研究团队一起对自己的教学进行分析。数据收集和分析将依赖于教室的视频分析、教师对任务执行的反思，以及在与教师和研究人员召开的研究小组会议上收集的数据，以分析实践。

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.